Recapitulation

September 8, 1997

"Fully diminished" chords. More about enharmonic ambiguity. The "fully diminished" chord is made out of only minor thirds, e.g. B-D; D-F; F-A flat. A flat-B is an augmented second whose size is 3 semitones, the same size as that of a minor third. The ambiguity here is fostered by the fact that, in the temperate tuning, A flat is equivalent to G#, B to C flat, F to E#, etc. Heard out of a tonal context (by itself, not following any other chords), it can not be identified as only one function in one key. As a matter of fact, the chord:

can be also spelled as:

The name "fully diminished" is useful for quick identification but, in terms of functional harmony, it's slang at best since it does not identify a tonal function. Such seventh chords may be built on the VII degree of any major or harmonic minor scale (ascending minor, too). Because of the enharmonic equivalent spellings noted above, the same chord can be VII in 4 different keys (both major and minor):

At the same time, similar chords ("fully diminished") can be built on two other scale degrees as chromatically altered chords: on II and on VI (see Piston for details).

Considering the possibility of spelling such a chord in at least four ways (root position and inversions), we realize that the B, D, F, A flat chord in our first example can be interpreted/resolved in 12 different keys:

Inversion:	      root      first     second       third
Function:  VII		C         A	  E flat	 F#      Dominant
           II+	      A flat      F         D            B       Sub-dominant
	   VI+        B flat      G         E            C#      Tonic

The use of such procedures in 19th. century music led eventually to the collapse of the tonal system: the strict, orderly, and hierarchical system can now accommodate a chord which can be any type of function (T, D, SD) and/or resolve in any key.

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